Correct Answer : Differential form of conservation equations used
Explanation : The normal shock wave analysis uses the control volume approach. The integral form of conservation equations are applied to the control volume. The flow is steady, adiabatic, without viscous effects and zero body forces.
Correct Answer : In the figure, a strong bow shock exists in front of the flow. The shock wave is curved around the blunt body, but the region of the shock closest to the nose is essentially perpendicular to the flow, i.e. region i is a normal shock.
Correct Answer : ρ1u1=ρ2u2
Explaination : The continuity equation of the normal shock equation is derived from the continuity equation of mass and is given as ρ1u1A1=ρ2u2A2. If the area of the control volume is same on both sides, it becomes ρ1u1=ρ2u2. The flow is steady and without viscosity.
Correct Answer : Speed of sound
Explanation : The speed of sound is the quantity that dominates the physical properties of compressible flow. Speed of light is not important in compressible flow problems. Density of medium and distance of propagation are secondary quantities.
Correct Answer : True
Explanation : This comes from the physical meaning of the Mach number. When we take the ratios of per unit mass kinetic energy to the potential energy of the fluid particle moving along a streamline, it comes proportional to the square of the Mach number. Thus, this is true.
Correct Answer : Speed of sound in incompressible medium is zero
Explaination : Incompressible flow is the limiting case of isentropic compressibility being zero. This gives an infinite speed of sound and a zero Mach number in that medium. Thus, theoretically, zero-Mach number flows are incompressible.
Correct Answer : False
Explanation : The given statement is false. For a perfect gas, the speed of sound is a pressure of temperature only. And hence, by changing pressure or density but keeping the temperature same, speed of sound will not change.
Correct Answer : Gas constant is same for both
Explanation : The sound of speed depends on gamma, T and the gas constant R for the respective gas. In case of helium and air, the gamma for helium is higher than air. Also, helium is lighter than air thus, R for helium being higher. This gives, at the same temperature, speed of sound more in helium than air.
Correct Answer : a0 is the stagnation speed of sound
Explaination : For a point in the flow, where the speed of sound is a, a0 is the stagnation speed of sound associated with that point. While a* is the sonic characteristic value associated with that same point. None of these is the maximum speed of sound in the flow.
Correct Answer : a* and a0 are constant along the entire flow for an adiabatic, inviscid, steady flow
Explaination : a* and a0 are the defined properties of the flow, constant at a point. They are related to each other but not same. For an adiabatic, inviscid, steady flow they are constant along the streamline. And if all the streamlines are coming from same uniform free-stream, they are constant along the entire flow.
Correct Answer : γ , M
Explaination : The stagnation and static temperatures for a calorically perfect gas are related with the equation Thus, it is clearly seen that this ratio depends on the gamma and the Mach number in the medium. It’s a very important relationship.
Correct Answer : Isentropic compression
Explaination : The defined properties of the flow P0 and ρ0 involve isentropic compression, which is adiabatic and reversible both. These properties are the values of the flow parameters when the flow is isentropically compressed to zero velocity, at a point with properties P and ρ.
Explanation : The defined M* or the characteristic Mach number depends upon the Mach number, for any given gamma. It changes if the Mach number is changed, which changes by changing the flow speed at any temperature. Hence, the given statement is false.
Explanation : At M = 6.3, the flow is termed as hypersonic. Due to this the additional flow properties related to hypersonic flow such as high temperature and low density effects comes into account. And because of these parameters the flow cannot be treated as perfect gas anymore.
Correct Answer : 0.724
Correct Answer : 6
Correct Answer : 2.71
Correct Answer : Adiabatic
Explanation : The flow across the normal shock wave is adiabatic as there is no heat transfer takes place during the process and the temperature increases due to the conversion of kinetic energy into internal energy across the shock wave.
Correct Answer : Decreases
Correct Answer : M = 1.0
Correct Answer : ΔP/P1
Explaination : As the flow passes through shock, its pressure increases. Hence the strength of the shock is governed by the ratio of the difference in pressure across the shock to upstream pressure and is defined as,(P2-P1)/P1 = ΔP/P1Therefore the larger the pressure difference across the shock, the stronger the shock is and vice versa.
Correct Answer : The total pressure remains constant
Explanation : Across the normal shock wave, the entropy increases, by second law of thermodynamics. It is a compression wave and the total pressure also changes. It is related to the entropy change inversely. Also, being an adiabatic flow, total temperature remains constant.
Correct Answer : Thermal dissipation there
Explanation : The flow across the normal shock wave is isentropic i.e. it is adiabatic also. Since, we are concerned with calorically perfect gases in an adiabatic, inviscid, steady flow the total temperature remains constant. Thermal dissipation is not a reason for total temperature being constant.
Correct Answer : Upstream Mach number
Explanation : Specifying a dimensionless quantity across the normal shock wave will specify all the other ratios and both the upstream and downstream Mach numbers. But for finding the velocity, temperature also needs to be specified and vice versa.
Correct Answer : \(\frac {T_2}{T_1}\)=1
Explaination : A Mach wave is a normal shock wave of diminishing strength. It occurs for M=1 upstream. Then downstream M=1 also. And all the ratios are equal to 1, i.e \(\frac {P_2}{P_1}\)=1, \(\frac {T_2}{T_1}\)=1, \(\frac {\rho_2}{\rho_1}\)=1. This can be found by calculation when we put m=1. The properties across Mach wave do not change.
Correct Answer : Mach number only
Explaination : The remarkable result for the normal shock wave is that for a given gas (given gamma), the Mach number ahead of the normal shock wave is a function of the Mach number ahead of the normal shock wave only, irrespective of pressure, density, temperature etc. The values are tabulated and found in gas tables for reference.
Correct Answer : Static pressure
Explaination : The velocity of sound can be calculated using the Pitot tube which measures the stagnation, also called total pressure and measuring the static pressure as well. There is no need to find temperature. And static velocity is nothing but zero velocity.
Correct Answer : Free-stream static pressure
Explanation : The Rayleigh Pitot tube formula helps to calculate the free- stream Mach number using the measured values of free-stream static pressure and Pitot pressure. It is based on the fact that a bow shock is formed at the mouth of the Pitot tube for a compressible supersonic flow. The Pitot pressure is the stagnation pressure behind the bow shock.
Explanation : The supersonic flow has a very high velocity. When it finds an obstruction in the form of a Pitot tube, a bow shock is formed for the supersonic flow over a blunt body. As a result, the stagnation pressure at the mouth of the Pitot tube is the pressure behind the bow shock.
Correct Answer : Thermodynamic properties
Explanation : Since the shock can be visualized as a thermodynamic device that compresses the gas, the Hugoniot relation only relates the thermodynamic quantities across the shock, without any reference to velocity and Mach number.
Correct Answer : Δe = -PavΔv
Explaination : The Hugoniot relation implies that “the change in internal energy is equal to the mean pressure across the shock times the change in specific volume.”i.e. e2-e1 = \(\frac {p_1+p_2}{2}\)(v1-v2)e2-e1 = –\(\frac {p_1+p_2}{2}\)(v2-v1)Δe = -PavΔv
Correct Answer : Hugoniot curve
Explaination : As in thermodynamic equilibrium state the specific energy can be expressed as a function of pressure and specific volume i.e.e = e(p, v)Then from the Hugoniot relation, p2 = f(p1, v1, v2)This means that for given p1 and v1, it represents p2 as a function of v2. And the plot of this relation in pv diagram is called Hugoniot curve, and such curve is the locus of all possible pressure-volume conditions behind the normal shocks of different strengths for given upstream p1 and v1.
Correct Answer : 1.254
Explaination : According to Hugoniot curve the pressure ratio and density ratio are related by;\(\frac {p_2}{p_1} = \frac {(\frac {γ+1}{γ-1})(\frac {v_1}{v_2})-1}{(\frac {γ+1}{γ-1})-(\frac {v_1}{v_2} )} \)Therefore for given flow properties \(\frac {2.6}{1.89}=\frac {6(\frac {v_1}{v_2})-1}{6-(\frac {v_1}{v_2}) }\)i.e. \(\frac {v_2}{v_1}\) = 1.254
Correct Answer : Both pressure and density increases
Explanation : A supersonic wave is termed as a detonation wave. Therefore in detonation heat and radial diffusion do not control the velocity, but the shock wave structure developed by the supersonic waves causes the flow to slow down, increasing its pressure, density, and temperature across the shock.
Correct Answer : 0 ≤ p ≤ ∞
Explaination : The Hugoniot curve represented by pv diagram asymptotically approaches to the linep = -(γ-1)/(γ+1)As a result of this, the entire range of pressure ratio occurs between zero and infinite, i.e. the pressure on the Hugoniot curve is bounded by 0 ≤ p ≤ ∞.
Correct Answer : Isentropic
Explanation : A sound wave is an infinitesimally small pressure wave. Hence the changes across the wave are very small and the speed of the process corresponding to these changes is very fast. Hence if there is no heat transfer in the system, the change in flow properties across the sound wave can be assumed as isentropic.
Correct Answer : Enthalpy ratio
Correct Answer : 410 m/s
Correct Answer : Weak shock
Explanation : For a very small pressure jump across the shock, P2 is just slightly higher than P1, and according to the relation of the strength of the shock(P2-P1)/P1 << 1Hence since there is a minor change in flow properties across the shock, such shock is called the weak shock.
Correct Answer : 4
Correct Answer : 242.85 m/s
Correct Answer : Zero
Explaination : As the shock gets reflected from the tub walls and travels back, the strength of the shock is such that the originally induced fluid motion with velocity behind the shock is completely stopped. Hence the fluid velocity behind the reflected shock becomes zero.
Correct Answer : Weaker
Explanation : As the flow passes through the incident wave its Mach number decreases as it moves downstream, i.e. M2 < M1. Now this M2 becomes the upstream Mach number M1 for the reflected wave, and since the deflection angles are the same for both incident and reflected waves, while reflected shock has lower upstream Mach number, the strength of the reflected wave is weaker than the incident wave.
Correct Answer : CR + Vp
Explaination : Since the shock represented in the figure is the reflected shock wave, as the shock moves upstream the velocity of gas relative to the shock wave is CR + Vp.
Correct Answer : β1 > β2
Explaination : As the wave gets reflected from the wall according to general shock characteristics, its Mach number decreases. Hence the reflected wave now has a lower upstream Mach number than the incident wave, due to which the reflected wave has a lower shock angle than an incident wave, i.e. β1 > β2.
Correct Answer : Pressure boundary condition
Explanation : When the Shock wave is incident on the open end, it either gets reflected into compression or expansion wave, to adjust the flow pressure with the boundary pressure. Hence for a shock wave reflection from the open end, the pressure boundary condition is satisfied.
Correct Answer : To increase the Mach number, we need to either decrease the internal energy or increase the kinetic energy
Explaination : According to relation, \(\frac {KE}{Internal \, Energy} = \frac {γ(γ-1) M^2}{2}\); it clearly shows that to increase Mach number we need to either decrease internal energy or increase kinetic energy.
Correct Answer : Both regions have same velocity and pressure but may have different density and temperature
Explanation : On the either side of the contact surface, the temperature and density may be different but it is necessary that the pressure and fluid velocity be the same, since contact surface is an imaginary boundary which separates high pressure gases from mixing with low pressure gases.
Correct Answer : If the flow is more than Mach number 0.3 or the percentage change in density is more than 5%
Explanation : Compressible effects are observed in all flow regimes but its effects are only significant from Mach number 0.3 or if the percentage change in density of the flow is more than 5%.
Correct Answer : When gases are thermally and calorically perfect
Explanation : Gases are said to be ideal when they are thermally and calorically perfect. When the specific heat capacity of the gas does not change and is constant, it is considered as calorically perfect. If internal energy and enthalpy is a function of temperature only then gas is said to be thermally perfect.
Correct Answer : 0.8254
Explaination : We know that p2 = p3 in a shock tube, so expansion strength is given by, \(\frac {p_3}{p_4} = \frac {p_2}{p_1} \times \frac {p_1} {p_4} = \frac {29.65}{35.92}\) = 0.8254.
Correct Answer : The relation between shock strength and diaphragm pressure ratio
Explanation : For shock tube operation, it is of prime importance to develop a relation between shock strength \(\frac {p_2}{p_1}\) and diaphragm pressure ratio \(\frac {p_4}{p_1}\). Once the shock strength is known, all other glow quantities can be found from the normal shock relations.
Correct Answer : Viscous stress and heat transfer
Explanation : Viscous stress and heat transfer are two non-equilibrium conditions observed across the flow due to high-temperature gradient and pressure gradient.
Correct Answer : 44.37°
Correct Answer : Zone of silence
Explanation : The region with all the disturbances inside the Mach cone of the moving body is called the zone of action. The region outside the Mach cone is known as the zone of silence where the objects are unaware of the disturbances. A control volume is any volume in space where analysis is conducted.
Correct Answer : The Mach number will become subsonic
Correct Answer : Collection of Mach waves
Explanation : Expansion waves are collection of infinite Mach waves which are diverging from a convex corner. They together form an expansion fan and the flow is isentropic across it.
Correct Answer : Shock angle decreases
Explanation : In θ-β-M relation, where θ represents wall deflection angle, β represents shock angle and M represents Mach number, it shows that with increasing Mach number and constant wall deflection angle, the shock angle decreases.
Correct Answer : Across a shock wave
Explanation : Entropy increase across a shock wave makes it an irreversible process. The entropy increase can be found out as it is a function of static temperature and pressure ratios across the normal shock.
Correct Answer : Non-isentropic
Explanation : Flow across a Mach wave follows an isentropic process. Isentropic process is characterized by its adiabatic and reversible process. Stagnation properties remains constant across the wave.
Correct Answer : There is a sudden change in flow direction at the body and pressure increases downstream of the shock
Explanation : When the flow is supersonic around a wedge, it is observed that there is a sudden change in flow direction at the body and pressure increases downstream of the shock.
Correct Answer : Finite disturbances will be introduced and the wave will be called a shock wave
Explanation : When the wedge angle is finite, direction of flow changes rapidly and this deviation causes shock wave. There is pressure increase across the shock wave but total pressure reduces since velocity reduces.
